Archimedean Prufer structures alias filter Archimedean d-semigroups

Inspired by the monograph of Larsen/McCarthy the author started a series of articles concerning abstract multiplicative ideal theory along the lines of [23]. In the present paper we turn to Archirnedean Prufer structures. that is to algebraic m-lattices satisfying the two implications (P) a(1) + ... + a(n) superset of or equal to B double right arrow a(1) + ... + a(n) \ B and (A) A(n) superset of or equal to B (For Alln is an element of N) double right arrow AB = B = BA. Since these properties imply commutativity we start from commutative structures without real loss of generality and give characterizations of arbitrary and also of special Archimedean Prufer structures.